[petsc-users] Compact finite differences

[Gaetano Esposito]

Compact finite differences have been already discussed in this post
and following responses:
http://lists.mcs.anl.gov/pipermail/petsc-users/2011-November/011006.html.

If I understand well, the matrix for a 2-D (or 3-D) *implicit* solver
that makes use of compact FD for the calculation of derivatives is not
"banded" because of the ordering of the x-y-z variables in the
solution vector destroys any structure, and the matrix is simply
sparse (bandwith=sqrt(n)). In that post is actually suggested that a
sparse dense solver could be more attractive because of that.

However, if the PDE's are solved explicitly in time, the derivatives
in all directions may be calculated independently by using an
efficient sequential algorithm (o(n)). I am not familiar with any
parallel implementations of the banded diagonal algorithm solvers, but
I was wondering whether this could be efficiently implemented in Petsc
with the existing MA modules. But at that point, I don't know whether
there will be any advantage in possibly using an iterative solver that
converges to the exact solution in N iterations for a well behaved
matrix as the one deriving from compact FD.

--g